In general, there are certain things available from YAML that are not available from JSON.

YAML is visually easier to look at. In fact the YAML homepage is itself valid YAML, yet it is easy for a human to read.
YAML has the ability to reference other items within a YAML file using "anchors." Thus it can handle relational information as one might find in a MySQL database.
YAML is more robust about embedding other serialization formats such as JSON or XML within a YAML file.
In practice neither of these last two points will likely matter for things that we do, but in the long term, YAML may be a more robust and viable data serialization format.